All operations would take place within Israeli territory, Israeli army spokesman Jonathan Conricus.
The Israeli army said on Tuesday it had detected Hezbollah tunnels infiltrating its territory from Lebanon and had launched an operation to cut them off.
Israeli army spokesman Jonathan Conricus said the "attack tunnels" detected were not yet operational.
He declined to say how many were detected or how they would be cut off.
All operations would take place within Israeli territory, Conricus said, though they were likely to boost tensions with Hezbollah, the Shia militant group with which Israel fought a devastating war in 2006.
The military has used various means to collapse or fill in tunnels from the Gaza Strip.
"We have launched Operation Northern Shield to expose and thwart cross-border attack tunnels dug by Hezbollah terror organisation from Lebanon into Israel," Conricus told journalists.
The announcement of the operation comes after Israeli Prime Minister Benjamin Netanyahu met US Secretary of State Mike Pompeo in Brussels on Monday night.
Netanyahu said he had planned to discuss with Pompeo "steps we are taking together to block the aggression of Iran and its proxies in the north," referring to Syria and Lebanon.
Hezbollah is backed by Iran, Israel's main enemy.